Publications and Preprints
[Interface of PDEs and Machine Learning]
Variational Actor-Critic Algorithms. [pdf]
Yuhua Zhu and Lexing Ying.
ESAIM: Control, Optimisation and Calculus of Variations, 2023.
A Note on Optimization Formulations of Markov Decision Processes. [pdf]
Lexing Ying and Yuhua Zhu.
Communications in Mathematical Sciences, 20(3):727–745, 2022.
The Vlasov Fokker Planck Equation with High Dimensional Parametric Forcing Term. [pdf]
Shi Jin, Yuhua Zhu*, and Enrique Zuazua.
Numerische Mathematik, 150(2):479–519, 2022.
Borrowing From the Future: Addressing Double Sampling in Model-free Control. [pdf]
Yuhua Zhu, Zachary Izzo and Lexing Ying
Mathematical and Scientific Machine Learning, pages 1099–1136, PMLR, 2022.
Why Resampling Outperforms Reweighting for Correcting Sampling Bias with Stochastic Gradients. [pdf]
Jing An, Lexing Ying, Yuhua Zhu*.
International Conference on Learning Representations (ICLR), 2021.
A Sharp Convergence Rate for a Model Equation of the Asynchronous Stochastic Gradient Descent. [pdf]
Yuhua Zhu, Lexing Ying.
Communications in Mathematical Sciences, 19(3), 851-863, 2020.
Borrowing From the Future: An Attempt to Address Double Sampling. [pdf]
Yuhua Zhu and Lexing Ying.
Mathematical and Scientific Machine Learning, PMLR 107:246-268, 2020.
On Large Batch Training and Sharp Minima: A Fokker-Planck Perspective. [pdf]
Xiaowu Dai and Yuhua Zhu*.
Journal of Statistical Theory and Practice (JSTP), special issue on "Advances in Deep Learning", 2020.
A Consensus-Based Global Optimization Method for High Dimensional Machine Learning Problems. [pdf]
Jose Carrillo, Shi Jin, Lei Li and Yuhua Zhu*
ESAIM: Control, Optimisation and Calculus of Variations 27, S5, 2020.
A Local Sensitivity and Regularity Analysis for the Vlasov-Poisson-Fokker-Planck System with Multi-dimensional Uncertainty and the Spectral Convergence of the Stochastic Galerkin Method. [pdf]
Networks and Heterogeneous Media, 14(4), 677-707, 2019.
An Uncertainty Quantification Approach to the Study of Gene Expression Robustness. [pdf]
Pierre Degond, Shi Jin and Yuhua Zhu*.
Methods and Applications of Analysis (A special issue in honor of the 80th birthday of Prof. Ling Hsiao), 2019.
Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales. [pdf]
Shi Jin and Yuhua Zhu*.
SIAM Journal on Mathematical Analysis, 50, 1790-1816, 2018.
The Vlasov-Poisson-Fokker-Planck System with Uncertainty and a One-Dimensional Asymptotic-Preserving Method. [pdf]
Yuhua Zhu and Shi Jin.
Multiscale Modeling and Simulation, 15, 1502-1529, 2018.
Continuous-in-time Limit for Bayesian Bandits. [pdf]
Yuhua Zhu, Zachary Izzo and Lexing Ying.
Submitted to Journal of Machine Learning Research.
Operator Augmentation for Model-based Policy Evaluation. [pdf]
Xun Tang, Lexing Ying and Yuhua Zhu*.
Under Minor Revision at Communications in Mathematical Sciences.
Stabilization of the Vlasov Fokker Planck Equation with Reflective Boundary Condition. [pdf]
Michael Herty, Shi Jin and Yuhua Zhu*.
Under Minor Revision at Mathematical Control and Related Fields.
Uncertainty Quantification for Fokker Planck Type Equations and Related Problems in Machine Learning. [pdf]
Ph.D. Thesis, Department of Mathematics, UW-Madison, 2019.